To prove this we need to recall the definition of the degeneracy maps of \(\overline{W}G\) . From [1]} we have
\(s_0(e) = 1\in G_0\)  if \(n=0\)  and
\(s_i(g_{n-1},\ldots , g_0) = {\left\lbrace \begin{array}{ll}(1,g_{n-1},\ldots , g_0)\qquad \text{if}\ i=0, \\(s_{i-1}(g_n),\ldots , s_0(g_{n-i+1}),1,g_{n-i},\ldots , g_0) \qquad \text{if}\ 1\le i\le n\end{array}\right.}\) 
